Symmetrized perturbation determinants and applications to boundary data maps and Krein-type resolvent formulas

DOI10.1112/PLMS/PDR024zbMath1247.34030arXiv1007.4605OpenAlexW1979450575MaRDI QIDQ2881022

Maxim Zinchenko, Friedrich Gesztesy

Publication date: 3 April 2012

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.4605

zbMATH Keywords

resolventSchrödinger operatortrace formulaseparated boundary conditionsKrein's spectral shift functionRobin-to-Robin boundary data mapsymmetrized Fredholm perturbation determinant

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Green's functions for ordinary differential equations (34B27) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (10)

Trace formulas for additive and non-additive perturbations ⋮ Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators ⋮ ON STABILITY OF SQUARE ROOT DOMAINS FOR NON‐SELF‐ADJOINT OPERATORS UNDER ADDITIVE PERTURBATIONS ⋮ On the index of a non-Fredholm model operator ⋮ On traces and modified Fredholm determinants for half-line Schrödinger operators with purely discrete spectra ⋮ Weak convergence of spectral shift functions for one‐dimensional Schrödinger operators ⋮ On index theory for non-Fredholm operators: A (1 + 1)-dimensional example ⋮ Lifshitz-Kreĭn trace formula for Hirsch functional calculus on Banach spaces ⋮ Perturbation determinants for singular perturbations ⋮ Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus

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